Optical system and display apparatus

ABSTRACT

A display apparatus which has a mirror with a free curved reflective surface of which curvature fluctuates with inflection points, a liquid crystal display (LCD), a back light and a polarizer. Light of an image which was modulated by the LCD is reflected by the free curved reflective surface and passes through the polarizer. Then, the light is directed to an optical pupil. Since the curvature of the free curved reflective surface fluctuates with inflection points, curvature of field and distortion can be corrected properly, and an image of high quality can be formed.

This application is based on Japanese patent application Nos.2002-279806 and 2003-72110, the contents of which are herebyincorporated by reference.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to an optical system, and moreparticularly to an optical system comprising a free curved reflectivesurface. The present invention also relates to a display apparatus, andmore particularly to a display apparatus which is suited to be used as ahead mounted type, which is called an HMD (head mounted display).

2. Description of Related Art

Japanese Patent No. 3155341 (reference 1) discloses a display apparatuswhich comprises an aspherical concave mirror of which curvature in theplane of incidence of the optical axis is set such that a plane imagecan be formed. Consequently, on the display, images of high picturequality can be seen.

U.S. Pat. No. 5,594,588 (reference 2) discloses a display apparatuswhich comprises an aspherical concave mirror of which curvature in adirection perpendicular to the plane of incidence of the optical axis isset such that distortion can be minimized. Consequently, on the display,images of high picture quality can be seen.

Japanese Patent Laid Open Publication No. 11-95160 (reference 3)discloses a head mounted display apparatus which comprises a half mirrorand a polarizer which is laminated on the half mirror. Thereby, thequantity of reflected light is reduced.

However, the display apparatus of the reference 1 has a problem thatcorrection of distortion is sacrificed for the sake of achieving a planeimage. More specifically, as FIG. 17 shows, a rectangular image 500 isreflected on a free curved reflective surface 501 to be directed to anoptical pupil 510, and a virtual image 505 is seen on the optical pupil510 as a distorted image 505′.

Also, the display apparatus of the reference 2 has a problem thatcorrection of curvature of field is sacrificed for the sake ofminimizing distortion or a problem that resolution is low. Morespecifically, as FIG. 18 shows, a rectangular image 500 is reflected ona free curved reflective surface 502 to be directed to an optical pupil510, and a virtual image 506 is seen on the optical pupil 510 as arectangular image 506′. Distortion was corrected, and the image 506 isrectangular. However, the curvature of field of the image 506′ is largeand more than 1 diopter, so that the image is difficult to see. Withthis free curved reflective surface 502, if it is tried to correctcurvature of field as well as distortion, the image 506′ will have a lowresolution and will be blurred.

In the display apparatus disclosed by the reference 3, a half mirror isused. Therefore, although the quantity of external light is reduced to ahalf, 25% of the quantity of light is reflected to be directed to theeyes of an observer, which makes the image difficult to see. Also,because only 25% of the quantity of light from the image is used, theimage is dark. Further, because the light from the image is reflected bythe half mirror, the apparatus is large.

Recently, various types of color image forming apparatuses have beendeveloped and provided. Color image forming apparatuses are generallydivided into a color filter type and a field sequential driving type.

FIG. 14 a shows a screen on which images A and B are displayed. FIG. 14b schematically shows display elements of the color filter type, andFIG. 14 c schematically shows display elements of the filed sequentialdriving type.

In the color filter type, a red color filter R, a green color filter Band a blue color filter B are provided for each pixel, and depending onthe luminous balance of the three filters, a color image is formed. Inthis type of color image forming apparatus, because one dot is formed byuse of three filters, a color shift in accordance with the pitch of thefilters occur. The color shift is so small that it will not be apractical problem in an apparatus which enables an observer to see theformed image directly. However, in an apparatus which magnifies a formedimage, such as an HMD, the color shift is also magnified, and thepicture quality will be lowered.

On the other hand, in the filed sequential driving type, as shown byFIG. 14 c and as disclosed by Japanese Patent Laid Open. Publication No.2001-117045 (reference 4) and Japanese Patent Laid Open Publication No.2001-188194 (reference 5), the illuminating light is switched among red,green and blue sequentially at a high speed, and synchronously, in eachpixel, the light of red, the light of green and the light of blue aremodulated in accordance with image signals of the respectivewavelengths. Consequently, a color image can be seen by an after imageeffect. As a modulating device, an LCD (liquid crystal display), a DMD(digital micromirror device) made by U.S. Texas Instruments Incorporatedor other suitable devices can be used.

In the field sequential driving type, an image of R, an image of G andan image of B are formed in one pixel sequentially, and a color shiftdoes not occur. When the color filter type and the field. sequentialdriving type are to form images of the same resolution, the necessarynumber of pixels in the field sequential driving type is one third ofthat in the color filter type. When the color filter type and the fieldsequential driving type have the same displaying area, the size of eachpixel of the filed sequential driving type is three times as large asthat of the color filter type, and the field sequential driving type hasa higher vignetting factor and can form brighter images.

In an optical system for magnifying a formed image and displaying themagnified image, an optical element which diverts a bundle of rays isnecessary, and a refraction element or a reflection element is used.With respect to diversions of bundles of rays by a refraction element,as FIG. 15 shows, a medium refracts a bundle of red rays R, a bundle ofgreen rays G and a bundle of blue rays B at different angles because themedium has different refractive indexes to the respective wavelengths ofR, G and B. Thereby, chromatic aberration is caused.

On the other hand, with respect to bends of bundles of rays by areflection element, as FIG. 16 shows, a reflective element reflects abundle of red rays R, a bundle of green rays G and a bundle of blue raysB at the same angle, and chromatic aberration is not caused. JapanesePatent Laid Open Publication No. 5-303054 (reference 6) discloses amagnifying optical system which uses a reflective surface with thischaracteristic. However, the reference 6 merely discloses the magnifyingoptical system.

SUMMARY OF THE INVENTION

An object of the present invention is to provide an optical system and adisplay apparatus which can form an image of high picture quality bycorrecting both curvature of field and distortion.

Another object of the present invention is to provide a displayapparatus which is small and light, which prevents incidence of externallight and which displays images of high picture quality.

Further, another object of the present invention is to provide a displayapparatus which does not cause a color shift and which is suited to beused as a head mounted display.

In order to attain the objects, an optical system according to a firstaspect of the present invention comprises a free curved reflectivesurface of which curvature fluctuates with inflection points.

In the optical system according to the first aspect, since the curvatureof the free curved reflective surface fluctuates with inflection points,curvature of field and distortion can be corrected properly, and imagesof high picture quality can be formed.

A display apparatus according to a second aspect of the presentinvention comprises: a display device which displays an image, and amagnifying optical system which directs an image displayed by thedisplay device to an observer's pupil and which enables the observer tosee the image as a virtual image, and the magnifying optical systemcomprises a free curved reflective surface of which curvature fluctuateswith inflection points.

A display apparatus according to a third aspect of the present inventioncomprises a light source which emits bundles of rays of differentwavelengths; an image forming device which forms a color image by afield sequential driving method in which while the image forming deviceis illuminated with the bundles of rays sequentially, the bundles ofrays are modulated in accordance with the respective wavelengths in eachpixel of the image forming device; and a magnifying optical system whichreflects the bundles of rays by the image forming device on a surfacewhich performs surface reflection to direct the modulated bundles ofrays to an observer's pupil.

In the display apparatus according to the third aspect, a color image isformed by a field sequential driving method, and bundles of rays ofdifferent wavelengths are modulated sequentially in each pixel.Therefore, a color shift does not occur. Also, the magnifying opticalsystem is composed of only a surface which performs surface reflection,and chromatic aberration is not caused. Consequently, according to thethird aspect, a display apparatus which does not cause a color shift canbe obtained.

The surface which performs surface reflection may be a free curvedreflective surface of which curvature fluctuates with inflection pointslike the one employed in the optical system according to the firstaspect.

A display apparatus according to a fourth aspect comprises: a displaydevice which displays an image; a magnifying optical system whichdirects light of the image displayed by the display device to anobserver's pupil as a virtual image; and a polarizer which is locatedbetween the magnifying optical system and an optical pupil of themagnifying optical system. In the display apparatus, the magnifyingoptical system is composed of one reflective surface, and the light ofthe image emitted from the display device is linearly polarized light.Further, the polarizer is arranged so as to transmit the linearlypolarized light. While unnecessary external light is cut by thepolarizer, a bright image can be displayed.

BRIEF DESCRIPTION OF THE DRAWINGS

These and other objects and features of the present invention will beapparent from the following description with reference to theaccompanying drawings, in which:

FIG. 1 is a schematic view of an optical system according to a firstembodiment of the present invention;

FIG. 2 is a graph which schematically shows the shape of a free curvedreflective surface which is used in the optical system according to thefirst embodiment;

FIG. 3 is a view of an optical path which shows correction of curvatureof field and distortion which are caused by the free curved reflectivesurface;

FIG. 4 is a schematic view of a display apparatus according to a secondembodiment of the present invention;

FIG. 5 is a schematic view of a display apparatus according to a thirdembodiment of the present invention;

FIG. 6 is a schematic view of a display apparatus according to a fourthembodiment of the present invention;

FIG. 7 is a schematic view of a display apparatus according to a fifthembodiment of the present invention;

FIG. 8 is a schematic view of a display apparatus according to a sixthembodiment of the present invention;

FIG. 9 is a schematic view of a display apparatus according to a seventhembodiment of the present invention;

FIG. 10 is a schematic view of a display apparatus according to a eighthembodiment of the present invention;

FIG. 11 is a schematic view of a display apparatus according to a ninthembodiment of the present invention;

FIG. 12 is a schematic view of a display apparatus according to a tenthembodiment of the present invention;

FIG. 13 is a schematic view of a display apparatus according to aeleventh embodiment of the present invention;

FIG. 14 a, b and c are illustrations of a color display apparatus, FIG.14 a showing a model of color images and FIGS. 14 b and 14 c showinglight modulating elements;

FIG. 15 is an illustration which shows diversions of bundles of rays byrefraction;

FIG. 16 is an illustration which shows diversions of bundles of rays byreflection;

FIG. 17 is an illustration which shows distortion occurring in aconventional display apparatus; and

FIG. 18 is an illustration which shows curvature of field occurring in aconventional display apparatus.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS

Optical systems and display apparatuses according to preferredembodiments of the present invention are described with reference to theaccompanying drawings.

First Embodiment; See FIGS. 1 and 2

FIG. 1 shows an optical system 100 according to a first embodiment ofthe present invention. The optical system 100 comprises a mirror 102with a free curved reflective surface 102 a. The numeral 101 denotes animage surface, and the numeral 103 denotes an optical pupil.

When the optical system 100 is used as an image pickup system, lightcoming from the optical pupil 103 is reflected by the free curvedreflective surface 102 a to be imaged on the image surface 101, and theimage is picked up by an image pickup device. When the optical system100 is used as an observing system, light on the image surface 101 suchas light displayed on a liquid crystal display (LCD) etc. is reflectedby the free curved reflective surface 102a to be directed to the opticalpupil 103. The light incident to the optical pupil 103 is directed to anobserver's eyes, and thereby, the observer can see a virtual image.

The shape of the free curved reflective surface 102 a is defined by thefollowing polynomial (1). According to the first embodiment, theconstants shown by Table 1 are used. $\begin{matrix}{{Z = {\frac{{cr}^{2}}{1 + {{SQRT}\left\lbrack {1 - {\left( {1 + k} \right)c^{2}r^{2}}} \right\rbrack}} + {\sum\limits_{j = 2}^{55}\quad{C_{j}x^{m}y^{n}}}}}{j = {{\left\lbrack {\left( {m + n} \right)^{2} + m + {3n}} \right\rbrack/2} + 1}}{z\text{:}\quad{sag}\quad{of}\quad{surface}\quad{in}\quad{parallel}\quad{to}\quad z\quad{direction}}{c\text{:}\quad{curvature}\quad{at}\quad{vertex}}{k\text{:}\quad{conic}\quad{constant}}{C_{j}\text{:}\quad{coefficient}\quad{of}\quad x^{m}y^{n}}} & {{Polynominal}\quad(1)}\end{matrix}$ TABLE 1 First Enbodiment C 0 free curved Y −1.93E−01 X2−1.31E−02 Y2 −1.25E−02 reflective X2Y −4.24E−05 Y3 −2.34E−05 X4−3.86E−06 surface X2Y2 −7.48E−06 Y4 −1.16E−06 X4Y 5.07E−08 (axially X2Y3−3.75E−07 Y5 −4.41E−09 X6 1.12E−08 asymmetric X4Y2 8.33E−08 X2Y43.66E−09 Y6 −1.48E−09 aspherical surface) X6Y 4.95E−10 X4Y3 8.87E−09X2Y5 2.43E−09 X6Y2 −4.75E−10 X4Y4 1.08E−10 X2Y6 −1.75E−11 X6Y3 −7.54E−11X4Y5 −1.79E−11 X6Y4 −4.86E−12 X4Y6 1.44E−12

In the first embodiment, because C=0, the reference curvature isinfinite, that is, the surface is plane. However, the referencecurvature may be finite. The free curved reflective surface 102 a isasymmetric in a direction parallel to the plane of incidence of theoptical axis (x=0) and is symmetric with respect to the plane ofincidence of the optical-axis in a direction perpendicular to the planeof incidence of the optical axis. Unlike an axially symmetric opticalsystem, a free curved reflective surface does not have a fixed opticalaxis, and here, the line connecting the center of the image surface 101to the center of the optical pupil 103 is defined as the optical axis Q(see FIG. 2).

FIG. 2 schematically shows the shape of the free curved reflectivesurface 102 a. The curvature of the surface 102 a fluctuates withinflection points. When the curvature of the surface 102 a in the ydirection in the plane of incidence of the optical axis is shown in they coordinate on the optical pupil 103, a curve with inflection points ata pitch p is drawn.

Now referring to FIG. 3, the advantage deriving from the feature of thepresent invention that the curvature of the free curved reflectivesurface fluctuates with inflection points is described. In thefollowing, axially asymmetric optical systems according to preferredembodiments of the present invention will be described. However, theadvantage deriving from this feature can be obtained also in axiallysymmetric optical systems, and here, a case of using an axiallysymmetric reflective surface in an observing system is described. FIG. 3is a schematic virtual view to simplify the description, and the actualcurvature and the actual shape are different from those in FIG. 3.

The points a′, b′ and c′ on a curved surface are points which receivethe principal rays coming from three points a, b and c on an imagesurface, respectively, and the respective distances between the points aand a′, b and b′, and c and c′ are La, Lb and Lc. The curvatures on theyz section of the surface at the points a′, b′ and c′ are Ra, Rb and Rc.The center of the pupil is P.

First, in order to enable an observer to see a virtual image withoutcurvature of field, the following condition must be fulfilled accordingto the Newton's formula. $\begin{matrix}\begin{matrix}\quad & {{1/{La}} \times {\left( {{Ra}/2} \right)/\left( {{{Ra}/2} + {La}} \right)}} \\ = & {{1/{Lb}} \times {\left( {{Rb}/2} \right)/\left( {{{Rb}/2} + {Lb}} \right)}} \\ = & {{1/{Lc}} \times {\left( {{Rc}/2} \right)/\left( {{{Rc}/2} + {Lc}} \right)}}\end{matrix} & (1)\end{matrix}$

In order to enable an observer to see a virtual image without distortionas well as without curvature of field, the sections of the curvedsurface at a plane including a line section a′P, at a plane including aline section b′P and at a plane including a line section c′P must besimilar to each other. In order to meet this condition and in order toprevent astigmatic differences in the vertical direction and in thehorizontal direction at the points a′, b′ and c′ so as to inhibit theresolution from becoming lower, the following condition must befulfilled.Ra=Rb=Rc  (2)

From the expressions (1) and (2), the following expression is derived.La=Lb=Lc  (3)

In conventional optical systems, even when a free curved surface is usedas a reflective surface, as well as when a spherical surface or anaspherical surface is used, varying the curvature of the reflectivesurface gradually is not enough to meet the conditions (2) and (3).

The curvature of the reflective surface is varied with inflection points(the curvature is getting larger and getting smaller repeatedly) so thatthe reflective surface will meet the conditions (2) and (3). Thereby,curvature of field and distortion can be corrected, and images of highpicture quality and with high resolution can be seen.

A curved reflective surface according to the present invention iscomposed of curved surfaces with curvatures which meet the condition(2), and the curvatures determine local powers. These curved surfacesare connected to each other via curved surfaces with a smaller or alarger curvature. Therefore, at portions of the curved surfaces with asmaller or a larger curvature, the resolution will be worse. However, ifthe curved reflective surface has inflection points at a smaller pitch pthan the effective pupil, the aberration of the light more than a halfof the whole light which is coming from the curved reflective surface tothe effective pupil is corrected, and therefore, the resolution can beinhibited from becoming lower.

Also, when display means which displays an image pixel by pixel, such asa liquid crystal display, is used, it is not necessary to keep highresolution continuously, and distortion and curvature of field can becorrected more effectively.

As has been described, this arrangement gives theabove-described-benefit to axially symmetric reflective surfaces.However, when this arrangement is applied to an axially asymmetricreflective surface, the benefit is more remarkable.

Further, an effective pupil means, in an image pickup system, theentrance pupil used for image pickup. In an observing system, theeffective pupil means the pupils of an observer, and if the pupils of anobserver are larger than the optical pupil, the effective pupil meansthe optical pupil.

According to the first embodiment, in an observing system, the effectivepupil is 3 mm, and the pitch p is 2.5 mm. The optical pupil 103 islarge, and specifically has a dimension of 12 mm in the x direction anda dimension of 6 mm in the y direction, so that an observer can see animage easily. The pupils of human beings are generally about 3 mm.

The pitch p of the inflection points of the curved reflective surface islarger in the peripheral portions because less quantity of lightreflected at the peripheral portion is used in the effective pupil. Inother words, the curved reflective surface has, in the center portionaround the optical axis Q, inflection points at a smaller pitch than theeffective pupil, and in the peripheral portions, the curved reflectivesurface has inflection points at a larger pitch than the effectivepupil.

When an observer sees an image displayed on display means, there may bethe following problems: the contrast of the image is lowered because ofincidence of external light; or the picture quality is lowered becauseof stray light.

In the following, in order to provide a display apparatus which cutsexternal light, which is small and light and which displays an image ofhigh quality, display apparatuses according to a second embodiment and athird embodiment are described.

Second Embodiment; See FIG. 4

A display apparatus 120A according to the second embodiment of thepresent invention comprises the above-described optical system 100according to the first embodiment of the present invention. In FIG. 4,the numeral 121 denotes a light-transmitting type liquid crystal display(LCD), the numeral 122 denotes a back light, and the numeral 123 denotesa polarizer.

The LCD 121 modulates light emitted from the back light 122 inaccordance with image data and displays an image with a polarization ina direction shown by arrow “A”. The image light is reflected by the freecurved reflective surface 102 a and passes through the polarizer 123which has a transmitting axis in a direction shown by arrow “B”. Then,the light is directed to the optical pupil 103. The light on the opticalpupil 103 is partly or entirely incident to the eyes of an observer, sothat the observer can see the image as a virtual image.

The entire display apparatus 120A except the polarizer 123 is arrangedin a case 129, and unnecessary external light is shut out. Because thepolarizer 123 absorbs light coming from directions perpendicular to thedirection B, the polarizer 123 transmits only a half of the quantity oflight coming from outside. Thus, the quantity of external light incidentto the display apparatus 120A is very small. Also, since the polarizingdirection A of the LCD 121 and the polarizing direction B of thepolarizer 123 correspond to each other, the image is not dark.

Third Embodiment; See FIG. 5

FIG. 5 shows a display apparatus 120B according to the third embodimentof the present invention. The display apparatus 120B is basically of thesame structure as the display apparatus 120A according to the secondembodiment, and the display apparatus 120B further comprises aquarter-wave plate 124 provided on a front surface of the LCD 121 and aquarter-wave plate 125 provided on a back side of the polarizer 123.

The quarter-wave plate 124 is located between the free curved reflectivesurface 102 a and the LCD 121, and the quarter-wave plate 125 is locatedbetween the free curved reflective surface 102 a and the polarizer 123.The quarter-wave plates 124 and 125 do not need to be bonded or stuckrespectively on the front surface of the LCD 121 and on the back side ofthe polarizer 123.

The quarter-wave plate 124 changes linearly (in the direction A)polarized light into clockwise polarized light. The quarter-wave plate125 changes counterclockwise polarized light into linearly (in thedirection B) polarized light. More specifically, the linearly (in thedirection A) polarized light emitted from the LCD 121 is changed intoclockwise polarized light by the quarter-wave plate 124, and theclockwise polarized light is reflected by the free curved reflectivesurface 102 a and turns into counterclockwise polarized light. Thecounterclockwise polarized light is changed into linearly (in thedirection B) polarized light by the quarter-wave plate 125, and thelinearly polarized light passes through the polarizer 123.

The quarter-wave plates 124 and 125 are arranged such that the directionB of the second linear polarization will correspond to the direction Aof the first linear polarization, and thereby, even if the respectivephases shift more or less, sufficient polarizing performance can beachieved.

In the third embodiment, the quarter-wave plates 124 and 125 areprovided for the purposes of minimizing the influence of external lightand of preventing a double image.

In the structure of the second embodiment shown by FIG. 4, a half of thequantity of external light passes through the polarizer 123 andreflected in the polarizer 123. Then, because the direction ofpolarization does not change, the reflected light passes through thepolarizer 123 and emerges outside toward the optical pupil 103.Consequently, unnecessary light is incident to the optical pupil 103.

In the third embodiment, the quarter-wave plate 125 is provided. In thestructure, external light which has come inside through the polarizer123 further passes through the quarter-wave plate 125 and reflectedthereby. Then, when the reflected light is to emerge outside through thepolarizer 123, the light has passed through the quarter-wavelength 125back and forth. Thereby, the direction of polarization is turned at 90degrees. Consequently, the light is absorbed by the polarizer 123 anddoes not emerge outside (toward the optical pupil 103).

This benefit of minimizing the influence of external light can beobtained by providing the quarter-wave plate 125 between the free curvedreflective surface 102 a and the polarizer 123. Also, by providing thequarter-wave plate 124 as well as the quarter-wave plate 125, the imageis prevented from being darker in addition to achieving the benefit ofminimizing the influence of external light.

In the structure of the second embodiment, the image light emitted fromthe LCD 121 is partly reflected by the side of the polarizer 123 whichis closer to the optical pupil and is further reflected by the otherside of the polarizer 123. Then, the light which has been reflected inthe polarizer 123 twice emerges outside through the polarizer 123, andconsequently, a double image is caused.

In the structure of the third embodiment comprising the quarter-waveplates 124 and 125, however, especially when the quarter-wave plate 125is bonded or stuck on the back side of the polarizer 123, the lightwhich has been reflected by the side of the polarizer 123 which iscloser to the optical pupil is reflected by the side of the quarter-waveplate 125 which is closer to the reflective surface 102. The light whichwas reflected by the side of the polarizer 123 which is closer to theoptical pupil and came to the side of the quarter-wave plate 125 whichis closer to the reflective surface 125 has passed through thequarter-wave plate 125 back and forth, and therefore, the direction ofpolarization has turned at 90 degrees. Consequently, the light isabsorbed by the polarizer 123, and a double image does not occur.

Fourth Embodiment; See FIG. 6

FIG. 6. shows a display apparatus 120C according to a fourth embodimentof the present invention. In the display apparatus 120C, a prism 200 isused. The numeral 210 denotes an LCD, and the numeral 220 denotes anoptical pupil. Image light displayed on the LCD 210 is incident to theprism 200 through an entrance surface 201. The light is entirelyreflected by a surface 202 and further reflected by a free curvedreflective surface 203 of which curvature fluctuates with inflectionpoints. Then, the light passes through the surface 202 and is incidentto the optical pupil 220. An observer receives the light of the opticalpupil 220 on his/her own pupils and sees a virtual image.

In the fourth embodiment, the entrance surface 201 and the surface 202of the prism 200 are free curved surfaces. However, the surfaces 201 and202 may be planes or spherical surfaces.

Fifth Embodiment; See FIG. 7

FIG. 7 shows a display apparatus 120D according to a fifth embodiment ofthe present invention. The display apparatus 120D is of a head mountedtype, and the display apparatus 120A according to the second embodimentis installed in a case 301. The case 301 is held before the eyes of anobserver by a forehead pad 302 and a holder 303.

The display apparatus installed in the case 301 may be the one accordingto the first embodiment or the one according to the third embodiment aswell as the one according to the second embodiment.

Next, display apparatuses according to a sixth through an eleventhembodiments of the present invention which do not cause chromaticaberration and which are suited to be used as a head mounted type aredescribed.

Sixth Embodiment; See FIG. 8

FIG. 8 shows a display apparatus 1A according to the sixth embodiment.The display apparatus 1A comprises a light source unit 2, an imageforming device 10 and a magnifying optical system 20.

The light source unit 2 comprises light emitting diodes 3R, 3G and 3B, aplanar illuminating mirror 4 and a diffusing plate 5. The light emittingdiodes 3R, 3G and 3B emit a bundle of red rays, a bundle of green raysand a bundle of blue rays, respectively, sequentially at specifiedintervals. Each of the bundles of rays is reflected by the illuminatingmirror 4 and illuminates the image forming device 10 via the diffusingplate 5.

In the image forming device 10, a light-transmitting type LCD is used asa light modulating device. Each of the pixels of the LCD is illuminatedby the bundles of rays with different wavelengths emitted from the lightemitting diodes 3R, 3G and 3B sequentially and modulates the respectivebundles of rays in response to the different wavelengths. In this way,the image forming device 10 forms a color image by a field sequentialdriving method. More specifically, the light modulating device, insynchronization with emitting of bundles of rays from the respectivelight sources 3R, 3G and 3B, forms monochromatic images at specifiedintervals at a high speed. Consequently, an observer can see a colorimage by an after image effect.

When an image is formed by a field sequential driving method, each pixeldisplays R, G and B images sequentially, and therefore, essentially, acolor shift is not caused. Also, compared with a color filter type, thevignetting factor is large.

The magnifying optical system 20 is composed of a concave reflectivemirror coated with metal 21. The light modulated by the image formingunit 10 is reflected by the concave reflective mirror 21 to be directedto the pupils P of an observer. Because the bundle of red rays R, thebundle of green rays G and the bundle of blue rays B are diverted by thereflective surface at the same angle (see FIG. 16), chromatic aberrationdoes not occur.

In the sixth embodiment, the concave reflective mirror 21 is an axiallyasymmetric aspherical surface, and the position and the constructiondata thereof will be shown in Table 2 later. The axially asymmetricaspherical surface of the reflective mirror 21 is of the same shape ofthe free curved reflective surface 102 a in the first embodiment.

Seventh Embodiment; See FIG. 9

A display apparatus 1A′ according to the seventh embodiment of thepresent invention is basically of the same structure as the displayapparatus 1A according to the sixth embodiment. In the display apparatus1A′, a polarizer 123 which was described in connection with the secondembodiment is provided between the magnifying optical system 20 and thepupil P.

The entire of the display apparatus 1A′ except the polarizer 123 isencased, and the function of the polarizer 123 and the benefits obtainedthereby are the same as described in connection with the secondembodiment.

Eighth Embodiment; See FIG. 10

FIG. 10 shows a display apparatus 1B according to the eighth embodimentof the present invention. In the image forming device 10 of the displayapparatus 1B, a reflective type LCD is used as a light modulatingdevice. The other components of the display apparatus 1B are the same asthose of the display apparatus 1A according to the sixth embodiment. InFIG. 10, these components are provided with the same reference numeralsprovided in FIG. 8, and the descriptions of these components areomitted. In the eighth embodiment, the concave reflective mirror 21 isaxially asymmetric aspherical surface, and the position and theconstruction data thereof are the same as those of the reflective mirror21 in the sixth embodiment and will be shown in Table 2 later.

In the eighth embodiment, since a reflective type LCD is employed in theimage forming device 10, the use of an illuminating mirror 4 is nolonger necessary. Thus, the light source unit can be structured compact.The use of a diffusing plate 5 is optional.

Also, the light emitting diodes 3R, 3G and 3B can be positioned fartherfrom the pupils of an observer, and an observer can fit the displayapparatus 1B on his/her head comfortably.

Ninth Embodiment; See FIG. 11

A display apparatus 1B′ according to the ninth embodiment of the presentinvention is basically of the same structure as the display apparatus 1Baccording to the eighth embodiment. In the display apparatus 1B′, apolarizer 123 which was described in connection with the secondembodiment is provided between the magnifying optical system 20 and thepupil P. Further, a quarter-wave plate 124 which was described inconnection with the third embodiment is provided in front of the imageforming device 10, and a quarter-wave plate 125 is provided on the backside of the polarizer 123.

The entire of the display apparatus 1B′ except the polarizer 123 isencased, and the polarizer 123 and the quarter-wave plates 124 and 125function in the same way and bring the same benefits as described inconnection with the third embodiment.

Tenth Embodiment; See FIG. 12

FIG. 12 shows a display apparatus 1C according to the tenth embodimentof the present invention. In the display apparatus 1C, the magnifyingoptical system 20 comprises a concave reflective mirror 21 and a planemirror 22. The display apparatus 1C comprises the other components ofthe display apparatus 1A according to the sixth embodiment, and in FIG.12, these components are provided with the same reference numerals asthose in FIG. 8.

In the tenth embodiment, the concave reflective mirror 21 is axiallyasymmetric aspherical surface, and the position and the constructiondata thereof will be shown in Table 3 later.

The display apparatus 1C according to the tenth embodiment operates inthe same way and brings the same benefits as described in connectionwith the sixth embodiment. Moreover, since the image light is reflectedby the plane mirror 22, the light source unit 2 can be positionedfarther from the pupils P of an observer, and an observer can fit thedisplay apparatus 1C on his/her head comfortably.

Eleventh Embodiment; See FIG. 13

FIG. 13 shows a display apparatus 1D according to the eleventhembodiment of the present invention. In the display apparatus 1D, themagnifying optical system 20 is composed of a concave reflective mirror23. The concave reflective mirror 23 is an rotational symmetricaspherical surface, and the position and the construction data thereofwill be shown in Table 4.

The display apparatus 1D comprises the other components of the displayapparatus 1A according to the sixth embodiment. In FIG. 13, thesecomponents are provided with the same reference numerals as those inFIG. 8, and the descriptions thereof are omitted. These componentsfunction in the same way and bring the same benefits as described inconnection with the sixth embodiment.

Definition, Position and Construction Data of Concave Reflective Surface

The concave reflective mirrors 21 which are used in the displayapparatuses according to the sixth through tenth embodiments are axiallyasymmetric aspherical surfaces (free curved reflective surfaces). Theaxially asymmetric aspherical surfaces are defined by addition of an XYpolynomial to a tenth polynomial based on a conic. The XY polynomial isdeveloped with x^(m)y^(n). The polynomial (1) is used. The position andthe construction data of the concave reflective mirrors 21 which areused in the sixth through ninth embodiments are shown in Table 2 below,and the position and the construction data of the concave reflectivemirror 21 which is used in the tenth embodiment are shown in Table 3below.

The concave reflective mirror 23 which is used in the eleventhembodiment is a rotational symmetric aspherical surface and is definedby the following polynomial (2). The position and the construction dataof the concave reflective mirror 23 which is used in the eleventhembodiment are shown in Table 4 below.

The construction data shown in Table 2, Table 3 and Table 4 are valuesin a global coordinate system of which origin is the center of pupil.The optical axis from the center of pupil to the reflective surface isZ, the vertical direction is Y, and the horizontal directionperpendicular to the Y direction is X. The positions of each surface inthe respective directions X, Y and Z are shown. The unit is millimeter.The slants of each surface when the axes X, Y and Z are supposed to beaxes of rotation are shown by A, B and C, respectively. The unit isdegree. $\begin{matrix}{{Z = {\frac{{ch}^{2}}{1 + {{SQRT}\left( {1 - {\left( {1 + k} \right)c^{2}h^{2}}} \right)}} + {Ah}^{4} + {Bh}^{6} + {Ch}^{8} + {Dh}^{10} + {Eh}^{12} + {Fh}^{14} + {Gh}^{16} + {Hh}^{18} + {Jh}^{20}}}{z\text{:}\quad{sag}\quad{of}\quad{surface}\quad{in}\quad{parallel}\quad{to}\quad z\quad{direction}}{c\text{:}\quad{curvature}\quad{at}\quad{vertex}}{k\text{:}\quad{conic}\quad{constant}}{A,B,C,D,E,F,G,H,{J\text{:}\quad 4{th}},{6{th}},{8{th}},{10{th}},{12{th}},{14{th}},{16{th}},{18{th}},{20{th}\quad{variable}\quad{coefficients}}}} & {{Polynominal}\quad(2)}\end{matrix}$ TABLE 2 Sixth and Seventh Embodiment radius of surfacecurvature material position and aspherical data 1 pupil INFINITY air X 0Y 0 Z 0 A 0 B 0 C 0 2 mirror INFINITY reflective X 0 Y 3.934 Z 49.717surface A 10.030 B 0 C 0 axially asymmetric Y −1.93E−01 X2 −1.31E−02 Y2−1.25E−02 aspherical surface X2Y −4.24E−05 Y3 −2.34E−05 X4 −3.86E−06X2Y2 −7.48E−06 Y4 −1.16E−06 X4Y 5.07E−08 X2Y3 −3.75E−07 Y5 −4.41E−09 X61.12E−08 X4Y2 8.33E−08 X2Y4 3.66E−09 Y6 −1.48E−09 X6Y 4.95E−10 X4Y38.87E−09 X2Y5 2.43E−09 X6Y2 −4.75E−10 X4Y4 1.08E−10 X2Y6 −1.75E−11 X6Y3−7.54E−11 X4Y5 −1.79E−11 X6Y4 −4.86E−12 X4Y6 1.44E−12 3 display INFINITYBK7 X 0 Y −10.210 Z 33.757 surface A 9.427 B 0 C 0

TABLE 3 Eighth Embodiment radius of surface curvature material positionand aspherical data 1 pupil INFINITY air X 0 Y 0 Z 0 A 0 B 0 C 0 2mirror INFINITY reflective X 0 Y −2.913 Z 40.609 surface A 4.052 B 0 C 0axially asymmetric Y −1.04E−01 X2 −1.14E−02 Y2 −1.10E−02 asphericalsurface X2Y −3.90E−06 Y3 1.17E−05 X4 −9.64E−07 X2Y2 −4.97E−06 Y4−4.88E−06 X4Y −1.63E−06 X2Y3 −1.26E−07 Y5 −3.29E−07 X6 −4.10E−08 X4Y21.42E−07 X2Y4 −2.69E−07 Y6 4.83E−08 X6Y 3.85E−08 X4Y3 5.61E−08 X2Y56.82E−08 X6Y2 −1.89E−09 X4Y4 −3.28E−09 X2Y6 −4.20E−09 X6Y3 −1.65E−09X4Y5 −1.11E−09 X6Y4 2.11E−10 X4Y6 7.23E−11 3 mirror INFINITY reflectiveX 0 Y −5.000 Z 25.000 surface A −25.000 B 0 C 0 4 display INFINITY BK7 X0 Y −12.272 Z 24.557 surface A 121.582 B 0 C 0

TABLE 4 Ninth Embodiment radius of surface curvature material positionand aspherical data 1 pupil INFINITY air X 0 Y 0 Z 0 A 0 B 0 C 0 2mirror INFINITY reflective X 0 Y −27.488 Z 45.655 surface A −28.723 B 0C 0 rotational K −0.09268 A −0.21E−05 B 0.16E−08 symmetrical C −0.63E−12D −0.19E−15 aspherical surface 3 display INFINITY BK7 X 0 Y −10.230 Z31.957 surface A 4.674 B 0 C 0

In the sixth through ninth embodiments, the angle of field of the screenis 14 degrees in the X direction and 10 degrees in the Y direction. Inthe tenth embodiment, the angle of field of the screen is 10.7 degreesin the X direction and 8 degrees in the Y direction. In the eleventhembodiment, the angle of field of the screen is 14 degrees in the Xdirection and 10 degrees in the Y direction.

When the angle of field in the horizontal direction (X direction) andthe angle of field in the vertical direction (Y direction) are differentfrom each other, it is preferred that the concave reflective mirror 21or 23 is decentered in the direction in which the angle of field issmaller. As the amount of decentration of a concave reflective mirrorbecomes larger, the aberration caused thereby becomes more remarkable.Therefore, if the concave reflective mirror is decentered in thedirection in which the angle of field is smaller, the amount ofdecentration is smaller, and the aberration caused thereby is weaker.

Other Embodiments

Although the display apparatuses according to the second, third andfourth embodiments are observing systems (optical systems for formingvirtual images), these apparatuses can be structured as image pickupsystems (optical systems for forming real images). The apparatusesaccording to the first through fifth embodiments are composed ofreflective optical elements. However, it also will bring benefits tocombine a lens or a diffraction optical element with the free curvedreflective surface according to the present invention. Especially when amirror is combined with a free curved reflective surface of whichcurvature fluctuates with inflection points, the benefits areremarkable. When light is incident to a mirror at a slant, generally,large aberration occurs. However, the free curved reflective surface cancorrect the aberration.

Various kinds of light sources can be used. In the sixth througheleventh embodiments, light emitting diodes are used as the lightsources R, G and B. However, a combination of a white light source withan RGB color filter wheel is possible, and in this case, while a bundleof red rays R, a bundle of green rays G and a bundle of blue rays B areselectively transmitted to illuminate the image forming devicesequentially.

Also, various kinds of illuminating systems can be used. In the sixth,tenth and eleventh embodiments, the illuminating system is composed of aplane mirror and a diffusing plate. However, a light guide may be used.By using a light guide, a thin and compact illuminating system can bestructured.

In the above-described embodiments, a light-transmitting type or areflective type LCD is used as the light modulating device of the imageforming device. However, various kinds of light modulating devices canbe used as long as they are driven by a field sequential driving method.Alternatively, a light modulating device which modulates the directionof reflection of light which is incident thereto, such as a DMD made byU.S. Texas Instruments Incorporated, can be used.

Further, as the magnifying optical system, not only a total reflectionmirror which has a metal coating totally but also a half reflectionmirror which has a metal coating partly to reflect a part of a bundle ofrays can be used. In a case of using a half reflection mirror, if atransparent material is used as the base of the mirror and if the backside of the mirror is shaped optimally to the shape of the surface, asee-through type with which the observer can see both the external worldand the displayed image can be structured.

Although the present invention has been described with reference to thepreferred embodiments, various changes and modifications are possible tothose who are skilled in the art. Such changes and modifications are tobe understood as being within the scope of the present invention.

1.-13. (canceled)
 14. A display apparatus comprising: a light sourcewhich emits bundles of rays of different wavelengths; an image formingdevice which forms a color image by a field sequential driving method inwhich while the image forming device is illuminated with the bundles ofrays sequentially, the bundles of rays are modulated in accordance withthe respective wavelengths in each pixel of the image forming device;and a magnifying optical system which directs light of the image formedby the image forming device to an observer's pupil by reflecting thelight on a surface which performs surface reflection.
 15. A displayapparatus according to claim 14, wherein the magnifying optical systemis composed of one concave reflective surface.
 16. A display apparatusaccording to claim 15, wherein the concave reflective surface is anaspherical surface.
 17. A display apparatus according to claim 15,wherein the concave reflective surface is an axially asymmetricaspherical surface.
 18. A display apparatus according to claim 15,wherein the concave reflective surface is decentered in a direction inwhich an angle of field is smaller.
 19. A display apparatus comprising:a display device which displays an image; a magnifying optical systemwhich directs light of the image displayed by the display device to anobserver's pupil as a virtual image; and a polarizer which is locatedbetween the magnifying optical system and an optical pupil of themagnifying optical system; wherein: the magnifying optical system iscomposed of one reflective surface; the light of the image emitted fromthe display device is linearly polarized light; and the polarizer isarranged so as to transmit the linearly polarized light.
 20. A displayapparatus according to claim 19, further comprising: a firstquarter-wave plate which is located between the display device and themagnifying optical system; and a second quarter-wave plate which islocated between the magnifying optical system and the polarizer, whereinthe first and second quarter-wave plates are arranged such that thepolarizer transmits the linearly polarized light emitted from thedisplay device.